Our final example weakens the above assumption on the distribution of the noise \(\xi \)  but requires an \(L_{4}\) –\(L_{2}\)  moment equivalence for the marginals \(\left\langle {\omega }, {X} \right\rangle \) . For related work proving excess risk bounds under similar moment equivalence assumptions see [1]}, [2]} and [3]}. The proof of the below proposition is based on controlling the lower tail of random quadratic forms using a result in [2]}. See Appendix  for details.
